When a user is suspended from a SE site, it's usually going to be to stop them from causing trouble and give them a time out. Currently the process doesn't suspend them from the sites meta, and gives them that avenue to continue to cause trouble.

Should a suspension on a site automatically suspend a user from their meta (and chat)?

I don't know that a suspension is always a good idea. It might be a good idea most of the time, but probably not every time. Sometimes the user will have legitimate questions about the circumstances surrounding suspension.

Instead, I think perhaps using the penalty box for their meta account might be better.

It would be interesting to see this expand to the chat rooms, as well.

If I recall correctly from earlier discussion in the chat, this is [status-completed], though possibly not intentionally. Users need rep of >5 to participate in per-site meta activity, but suspended users' reputations are administratively set to 1 for the duration of the suspension, effectively disqualifying them.

@JeffAtwood, during the recent issue discussed in moderator chat, there seemed to be a notable period of time where a user who had 1 rep on the main site still had more than 500 rep on meta. Is this just because it takes some amount of time to sync the rep?
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C. RossOct 3 '10 at 11:40